When talking to parents, do you use です instead of だ and ます forms of verbs? I know that you don't do that stuff when talking to friends and people you know well and I definitely know my parents well, but is it disrespectful to use casual language?

From what I've read, children don't really learn desu/masu form until school. I don't think desu/masu is usually used in a family situation, though you use respectful terms when addressing parents and older siblings (okaasan, otousan, oneesan, oniisan).

If you're homestaying (is this even a word? Lol), I think it's acceptable to tone your Japanese down a little because as richvh wrote, kids, even adults, talk to their parents in casual Japanese. Personally, when talking to my Japanese friends' parents, I always use desu/masu. I would show the same respect to my friends' parents back home as well.